The industrial value of the synthesis of optically active substances, catalyzed by transition metal complexes containing chiral ligands, is well known. However, on account of the creation of at least one asymmetric center in an organic molecule, such catalytic reactions present great difficulty and are controlled industrially in only very special cases. Thus, it is known (U.S. Pat. Nos. 4,005,127, 4,142,992 and 4,220,590) that 3-(3,4-dihydroxyphenyl)alanine (L-DOPA) can be prepared by hydrogenation of 3-methoxy-4-acetoxyacetamidocinnamic acid with the aid of a homogeneous catalyst based on rhodium coordinated with a phosphorus ligand, followed by hydrolysis. However, the synthesis of this ligand requires a series of five stages, among them a separation of diastereoisomers, which consequently increases the overall prime cost of the procedure (B. D. VINEYARD, W. S. KNOWLES and M. J. SABACKY, Journal of Molecular Catalysis, 19 (1983) p. 161). It will be recalled that L-DOPA is used as the active principle in the treatment of Parkinson's disease. Vol. 23, No. 29 (1982), pages 2995-96, have described the asymmetric hydrogenation, at 20.degree. C. and under atmospheric pressure, of .alpha.-N-acetaminoacrylic acid, .alpha.-N-acetaminocinnamic acid, and itaconic acid in the presence of a cationic complex of the formula Rh(COD)L ClO.sub.4, in which COD denotes cyclooctadiene and L denotes the ligand N-(diphenylphosphino)-2-diphenylphosphinoxymethyl)pyrrolidine. E. CESAROTTI, A. CHIESA et al, have further described, in Journal Of Organometallic Chemistry, Vol. 251 (1983), pages 79-91, the asymmetric hydrogenation of .alpha.-N-acetaminocinnamic acid in the same conditions as above. However the optical yield in N-acetyl-(S)-phenylalanine that is obtained under such conditions is limited to 78% and the difficult problem of separating diastereoisomers is again encountered.